If you're not sure how maths is relevant to real life, then go to see this year's popular lectures put on by the London Mathematical Society. Kevin Buzzard of Imperial College will explore the digitisation of our lives — the fact that many of the things we enjoy and work with are now stored on computers which reduce them to numbers. This has weird consequences. For example, some numbers are copyrighted, and there are even some illegal prime numbers. But way before this digital revolution, mathematicians realised that numbers could encode all of mathematics (even the parts of it that aren't about numbers), and this has some even stranger consequences.
How do diseases spread?
Julia Gog, of the University of Cambridge, will look at how mathematics has been applied to help understand and control infectious diseases, from the scale of a single virus particle through to a global influenza pandemic, and some mathematical challenges for the future.
The lectures will take place on Wednesday 9th July at the Institute of Education in London (7:00pm) and again on
Wednesday 24th September at the Haworth Lecture Theatre, University of Birmingham (6:30pm). They are free, but if you wish to attend, please write to firstname.lastname@example.org. A form for registration is available on the LMS website.
Yesterday cosmologists at the University of Cambridge delivered their verdict on a major breakthrough that rocked science this week: the announcement of the BICEP2 project of direct evidence for an inflationary theory of the Universe and the existence of gravity waves (see here for our report). Having caught their breath, the Cambridge scientists carefully studied the results published by BICEP2 and presented their thoughts to a packed lecture theatre at the Institute of Astronomy.
The verdict was positive. "I don't see anything particularly fishy," said cosmologist Anthony Challinor. "There are niggles and there will always be with these kinds of data sets. But it all looks ok to me."
That's good news for the BICEP2 project, but there may be even more exciting news for cosmology as a whole. Challinor and George Efstathiou, his co-presenter at yesterday's talk, both work on the Planck mission, which uses a space based telescope to map the cosmic microwave background (find out more here). The trouble is that there's tension between Planck's results and those of BICEP2. Planck data concerning temperature fluctuations in the early Universe seem to suggest that there aren't any gravitational waves at all. BICEP2 data, looking at polarisation of light, suggest that there are. So if BICEP's conclusions are correct, physicists may need to look for new physics to explain the discrepancy. The detection of gravity waves is intimately linked to the idea that the Universe experienced a rapid period of accelerated expansion, called inflation, in the distant past, so it's inflationary theories that will come under scrutiny.
"The BICEP2 results have been an absolute triumph for the theory of inflation," says Challinor. "But the problem now is that the simplest models of inflation don't actually seem to fit. It's almost like we know less about inflation than we did before. What we need now is independent confirmation [of the results] from another experiment. If we see that, then it could well mean that we need new physics [to explain the results]." It looks like cosmology is heading for exciting times!
We love every number here at Plus equally (ok, not really, 3 and i are the best numbers), but there is no denying the fame, ubiquity and usefulness of the number . Today, written as 3.14 in US date format, is known as Pi Day, and we are celebrating with this lovely image created by Mick Joyce.
Graphic representation of , created by Mick Joyce
Joyce wrote a computer programme to create the image, with each of the digits in the decimal expansion of represented by a different coloured pixels, demonstrating that the expansions is essentially without repeats or structure. Joyce's page is one of our favourites from the upcoming book, 50 Visions of Mathematics. The book (which we were lucky enough to help edit) will be released in May to coincide with the 50th anniversary of the Institute of Mathematics and its Applications, but you can preorder it now!
This year, we hope to discuss this again with the current IMU president, Ingrid Daubechies, the first woman to hold this position. One of our favourite lectures at the 2010 conference was by Irit Dinur, will she be in line for the prize this year? We are looking forward to interviewing all the winners this year, but we must admit, as two female mathematicians ourselves, we will be incredibly excited if one or more of them are women!
Snowboarders are vulnerable to gravity. Image: Picswiss.ch.
How do you test the effects of gravity? One way is to tip yourself over the edge of your snowboard as you are elegantly gliding along to see how long it takes until you hit the ground. We tried that last week, but it didn't work (the Plus scientist contracted concussion). Another is to win a £4.2 million grant to develop sensitive equipment to detect elusive gravitational waves. This is what the University of Glasgow has just done, having applied for the funding from the Science & Technology Funding Council.
The Glasgow experiment will significantly extend our own using the snowboard. Had it been successful, our experiment would probably have confirmed Newton's universal law of gravitation, which says that the gravitational force between two point masses is
where and are the two bodies’ respective masses, is the distance between them and is the gravitational constant, approximately equal to . From this you can work out how long it should take a falling snowboarder to meet the snow face-on. The Glasgow experiment, however, will test a more sophisticated theory.
Newton came up with his law in 1687 and it remained unchallenged until 1905, when Einstein published his special theory of relativity. The theory says that there is a universal speed limit in the Universe: nothing can travel faster than light, that is, nothing can travel faster than roughly 300,000 metres per second. According to Newton, however, the effect of gravity is instantaneous. Take away the Sun, and the effect will be felt on Earth immediately. Einstein himself later remedied this problem by proposing that gravity isn't a force that wafts across the ether in some mysterious way, but a result of the curvature of space. An analogy that is often given is that of a bowling ball sitting on a trampoline. The ball creates a dip in the trampoline, curving its surface, so a marble placed nearby will roll into the dip towards the ball. According to Einstein, massive bodies warp space in a similar way, causing less massive bodies to be attracted to them.
One of the consequences of Einstein's theory of gravity is that when gravitational monsters such as black holes shunt their weight around, they should create ripples that can be felt across space and time. "Near black holes the curvature of spacetime is extremely high," explains Bangalore Sathyaprakash, a gravity expert. "Now imagine two black holes moving around each other: the curvature is large but also changing. It's a bit like taking a stick and moving it around in a pond. That's going to generate ripples in the water. Only in the case of black holes, we're talking about ripples in the very fabric of spacetime." These ripples are the gravitational waves researchers at the University of Glasgow will be looking for. They will develop instrumentation for gravitational wave detectors with a sensitivity of around 1/1000th of the diameter of a proton (10-18m).
Sheila Rowan, Professor of Physics and Astronomy at the University of Glasgow, said: "We are entering a very exciting time in the search for gravitational waves. Experiments aimed at detecting gravitational waves have been in development for several decades and we are now reaching sensitivity levels where detection is expected in the next few years." We hope they won't come away with concussion!
We've read the book. We've bought the T-shirt. And now, finally, here it is: the movie of one of our favourite maths problems, the bridges of Königsberg. Though admittedly, we made it ourselves. We learnt several interesting lessons in the process. For example that a bin doesn't make a good supporting character and that people who shouldn't be in the frame should get out of it. But other than that, we're well on course for an Oscar this weekend!
You can read more about the bridges of Königsberg here.